05666nam 2200769 a 450 991013974130332120200520144314.01-283-37237-197866133723761-118-46737-X0-470-72213-4(CKB)2550000000073863(EBL)698224(OCoLC)768731745(SSID)ssj0000566782(PQKBManifestationID)11349962(PQKBTitleCode)TC0000566782(PQKBWorkID)10552498(PQKB)11681057(MiAaPQ)EBC698224(Au-PeEL)EBL698224(CaPaEBR)ebr10518735(CaONFJC)MIL337237(PPN)188938516(EXLCZ)99255000000007386320080904d2008 uy 0engur|n|---|||||txtccrStochastic simulation and applications in finance with MATLAB programs[electronic resource] /Huu Tue Huynh, Van Son Lai and Issouf SoumaréChichester, England ;Hoboken, N.J. John Wiley & Sonsc20081 online resource (356 p.)Wiley financeDescription based upon print version of record.0-470-72538-9 Includes bibliographical references and index.Stochastic Simulation and Applications in Finance with MATLAB® Programs; Contents; Preface; 1 Introduction to Probability; 1.1 Intuitive Explanation; 1.1.1 Frequencies; 1.1.2 Number of Favorable Cases Over The Total Number of Cases; 1.2 Axiomatic Definition; 1.2.1 Random Experiment; 1.2.2 Event; 1.2.3 Algebra of Events; 1.2.4 Probability Axioms; 1.2.5 Conditional Probabilities; 1.2.6 Independent Events; 2 Introduction to Random Variables; 2.1 Random Variables; 2.1.1 Cumulative Distribution Function; 2.1.2 Probability Density Function2.1.3 Mean, Variance and Higher Moments of a Random Variable2.1.4 Characteristic Function of a Random Variable; 2.2 Random vectors; 2.2.1 Cumulative Distribution Function of a Random Vector; 2.2.2 Probability Density Function of a Random Vector; 2.2.3 Marginal Distribution of a Random Vector; 2.2.4 Conditional Distribution of a Random Vector; 2.2.5 Mean, Variance and Higher Moments of a Random Vector; 2.2.6 Characteristic Function of a Random Vector; 2.3 Transformation of Random Variables; 2.4 Transformation of Random Vectors2.5 Approximation of the Standard Normal Cumulative Distribution Function3 Random Sequences; 3.1 Sum of Independent Random Variables; 3.2 Law of Large Numbers; 3.3 Central Limit Theorem; 3.4 Convergence of Sequences of Random Variables; 3.4.1 Sure Convergence; 3.4.2 Almost Sure Convergence; 3.4.3 Convergence in Probability; 3.4.4 Convergence in Quadratic Mean; 4 Introduction to Computer Simulation of Random Variables; 4.1 Uniform Random Variable Generator; 4.2 Generating Discrete Random Variables; 4.2.1 Finite Discrete Random Variables4.2.2 Infinite Discrete Random Variables: Poisson Distribution4.3 Simulation of Continuous Random Variables; 4.3.1 Cauchy Distribution; 4.3.2 Exponential Law; 4.3.3 Rayleigh Random Variable; 4.3.4 Gaussian Distribution; 4.4 Simulation of Random Vectors; 4.4.1 Case of a Two-Dimensional Random Vector; 4.4.2 Cholesky Decomposition of the Variance-Covariance Matrix; 4.4.3 Eigenvalue Decomposition of the Variance-Covariance Matrix; 4.4.4 Simulation of a Gaussian Random Vector with MATLAB; 4.5 Acceptance-Rejection Method; 4.6 Markov Chain Monte Carlo Method (MCMC)4.6.1 Definition of a Markov Process4.6.2 Description of the MCMC Technique; 5 Foundations of Monte Carlo Simulations; 5.1 Basic Idea; 5.2 Introduction to the Concept of Precision; 5.3 Quality of Monte Carlo Simulations Results; 5.4 Improvement of the Quality of Monte Carlo Simulations or Variance Reduction Techniques; 5.4.1 Quadratic Resampling; 5.4.2 Reduction of the Number of Simulations Using Antithetic Variables; 5.4.3 Reduction of the Number of Simulations Using Control Variates; 5.4.4 Importance Sampling; 5.5 Application Cases of Random Variables Simulations5.5.1 Application Case: Generation of Random Variables as a Function of the Number of SimulationsStochastic Simulation and Applications in Finance with MATLAB Programs explains the fundamentals of Monte Carlo simulation techniques, their use in the numerical resolution of stochastic differential equations and their current applications in finance. Building on an integrated approach, it provides a pedagogical treatment of the need-to-know materials in risk management and financial engineering. The book takes readers through the basic concepts, covering the most recent research and problems in the area, including: the quadratic re-sampling technique, the Least Squared Method, the dWiley finance series.FinanceMathematical modelsStochastic modelsFinanceMathematical models.Stochastic models.332.01/51923332.0151923DAT 306fstubMAT 605fstubQP 890rvkST 601 M35rvkWIR 160fstubHuynh Huu Tue611231Lai Van Son611232Soumaré Issouf611233MiAaPQMiAaPQMiAaPQBOOK9910139741303321Stochastic simulation and applications in finance with MATLAB programs1137149UNINA